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Number of lattice paths starting at {n}^10 and ending when any component equals 0, using steps that decrement one or more components by one.
2

%I #7 Oct 16 2015 12:21:30

%S 1,1023,208994018773,3864094036317649535283,

%T 198305312034897003898098826655121,

%U 16102861078300336871094550725929002523470383,1698612808615154132767781717350125427082238529142835109,212216707280526234296212923289763064481087995125148762713351022339

%N Number of lattice paths starting at {n}^10 and ending when any component equals 0, using steps that decrement one or more components by one.

%H Alois P. Heinz, <a href="/A263168/b263168.txt">Table of n, a(n) for n = 0..10</a>

%p g():= seq(convert(n, base, 2)[1..10], n=1025..2047):

%p b:= proc(l) option remember;

%p `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))

%p end:

%p a:= n-> b([n$10]):

%p seq(a(n), n=0..5);

%Y Column k=10 of A263159.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 11 2015